I am repairing a 25-year-old bride hat for a fashion show. It needs to be reshaped. What do you have in your quilting kits that would stiffen it without making it yellow? It is sitting on a bowl, the top and the brim have to be sprayed and reshaped. I am thinking out spraying it with glue or starch.

Two ideas for you---
Lots of steam. Use a thin press cloth between iron and hat. Stuff hat with clean towels.

Also, to stiffen it dissolve water soluable embroidery stabilizer to make a starch-like product. Soak the hat fabric with it. Reshap hat as it dries. You could hasten the drying with a blow dryer set on low temp.